Chapter 2

Summarize the Reading 1D Kinematics, Lesson 1 (Method 2a)

• Lesson 1
• Summary
  1. What (specifically) did you read that you understand well? Describe at least 2 items fully.
     • I understood speed and velocity. Speed is how fast an object is going ignoring direction and velocity is how fast an object is going and it MUST include direction. Also, Scalars include things such as speed and distance. Vectors include direction such as velocity and displacement.
  2. What (specifically) did you read that made you feel little confused/unclear/shaky, but further reading helped to clarify? Describe the misconception(s) you were having as well as your new understanding.
     • Vectors confused me at first, but as I read on I realozed from the examples what they were. The direction part of confused me.
  3. What (specifically) did you read that you don’t understand? Please word these in the form of questions.
     • How does average speed work?
     • How do you set up the formulas and do the math to figure it out?
  4. What (specifically) did you read that you thought was pretty interesting, that you didn't know before, or can easily apply to your every day life?
     • I though the concept of velocity was very interesting. Now, I can apply velocity to my everyday life and understand the simple physics in the daily actions that I do each day.

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Class Notes: Constant Speed
Constant Speed

• Instantaneous Speed: the speed at any instant in time
• Average Speed: the average of all the Instantaneous speeds; found by distance/ time ratio
• Acceleration: change in velocity
• 4 different types of motion (Motion diagrams):
  • At rest
    • v=0
    • a=0
  • Constant speed:
    • --> --> -->
    • a=0
  • Increasing speed:
    • --> ----> ------->
    • ---> (Acceleration points in the same direction as velocity)
  • Decreasing speed:
    • ------> ----> --->
    • <--- (acceleration points opposite direction from velocity)
• Formulas:
  • Average Speed= total Distance Traveled/ total Time of Travel (speed for the whole trip)
  • Constant Speed: keep one speed the entire time (unchanging speed)
  • Average Velocity= Change in position/ time = displacement/ time
  • V= d/t

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Summarize the Reading: 1D Kinematics, Lesson 2 (Method 2a)

• After reading the material, answer the following questions:
  1. What (specifically) did you read that you already understood well from our class discussion? Describe at least 2 items fully.
  • I understood the ticker tape diagram. Dots that have a constant distance between them have a constant speed. Dots that have distances that get larger between each dow means that there is acceleration
  • Also, I understood vector diagrams from class. We discussed that if the arrow is getting larger then the velocity is increasing. If the arrows are getting smaller then the velocity is decreasing.
  1. What (specifically) did you read that you were a little confused/unclear/shaky about from class, but the reading helped to clarify? Describe the misconception you were having as well as your new understanding.
  • I understood everything we went over in class, however, the reading made me positive that I understood from class today.
  1. What (specifically) did you read that you still don’t understand? Please word these in the form of a question.
  • I understand everything in the reading. It is all pretty clear.
  1. What (specifically) did you read that was not gone over during class today?
  • I read that vector diagrams are used for not only acceleration, but to represent force and momentum too.

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Lab: Speed of a CMV

Materials:
- spark timer + tape
- meter stick
- masking tape
- CMV


Purpose and Objectives:
1. How precisely can you measure distances with a meterstick?
hypothesis: I can measure it to the millimeter.
2. How fast does your CMV move?
hypothesis: I believe my CMV moves about 89.41cm/s.
3. What information can you get from a position-time graph?
hypothesis: The information that you can get from a position- time graph is where the car is at an exact time.

Length of my laptop: 32.75 cm

Data Table: Position vs. Time

Graph


Analysis: The y is the change in position and the x is the change in time. The shape of the graph is a constant speed that is why it is a straight line. Average speed is found by dividing change in position (Y) by time (x).

Discussion Questions
1. Why is the slope of the position- time graph equivalent to average velocity?

• The slope for the position time graph is the equal to the change in position (y) divided to the change in time (x). The formula for average velocity is the change in position divided by the change in time and they are the same.

2. Why is it average velocity and not instantaneous velocity? What assumptions are we making?

• It is average velocity because in this lab we were finding the speed of the CMV through time not at one set time. Instantaneous velocity is the velocity at one set time. We are assuming that the vehicle is moving at a constant speed.

3. Why was it okay to set the y- intercept to zero?

• It is okay to set the y- intercept to zero because we started our experiment at the point zero and the x intercept was starting at zero too.

4. What is the meaning of the R2 value?

• The R2 value shows the trend-line's ability to pass through all the points on the graph. This shows the accuracy of the trend-line.

5. If you were to add the graph of another CMV that moved more slowly on the same axes as your current graph, how would you expect it to lie relative to yours?

• Since this CMV will move more slowly than my car, I would expect it to lie lower (have a lower slope) than my slope on the graph.

Conclusion

• My hypothesis was for my cart to move at 89.41 cm/s, which was no where close to my results. In the lab, my car moved at 17.71 cm/s and I did not use any evidence in my hypothesis to attempt to get the right results. The sources of error that may have contributed to inaccuracies were things such as an unleveled surface, measuring inaccurate with the meter stick, or starting the cart before the timer. These issues could have been prevented if we took a level to the lab desk to make sure it was flat. Instead of using a meter stick, we could have used a measuring tape which would have prevented the issues of having a flat tape to compare to the flat spark tape and not have the issue of going over 50 cm. Also, If you started the car before the timer the dots may have not been a constant distance from each other and you would have had less data.

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Class Activity: Graphical representations of Equilibrium

1. How can you tell that there is no motion on a…
   1. position vs. time graph- If the line has a slope of zero
   2. velocity vs. time graph- If the line has a slope of zero
   3. acceleration vs. time graph- If the line has a slope of zero

1. How can you tell that your motion is steady on a…
   1. position vs. time graph- There would be a constant slope with a straight line with no outliers
   2. velocity vs. time graph- The velocity would remain the same constant slope also. It would be a straight line.
   3. acceleration vs. time graph- Then the graph would be a straight line because there is no acceleration

1. How can you tell that your motion is fast vs. slow on a…
   1. position vs. time graph- it would be faster or greater if the slope was steeper and slower if it was less steep.
   2. velocity vs. time graph- It would be faster if it was more positive or negative and slower if it was less positive or negative.
   3. acceleration vs. time graph- If the graph has a steep slope it is going fast, however, if the graph is has a less steep slope it is going slow.

1. How can you tell that you changed direction on a…
   1. position vs. time graph- If you are walking away from the sensor it is a positive slope and if you are walking towards the sensor, it has a negative slope.
   2. velocity vs. time graph- if you are walking straight in a positive direction the slope of the line will be positive and if you are walking backward in a negative direction the slope of the line will be negative.
   3. acceleration vs. time graph- It depends if the slope is positive or negative.

1. What are the advantages of representing motion using a…
   1. position vs. time graph- It is a simple way to see how far you have gone in a certain amount of time.
   2. velocity vs. time graph- By looking at the graph you can see the change in direction
   3. acceleration vs. time graph- you can see exactly where the graph started to accelerate.

1. What are the disadvantages of representing motion using a…
   1. position vs. time graph- The data may not always be accurate. For example, if the person is swaying their arms there will be an outlier, or if the sensor does not line up with the middle of your abdomen the results will be altered.
   2. velocity vs. time graph- The information may not always be correct. If the sensor does not line up with your body, it may not catch any data, or it may catch other moving objects.
   3. acceleration vs. time graph- the data may not be correct or you could read the graph wrong
   4. 
   5. acceleration vs. time graph

1. Define the following:
   1. No motion is when the object is at rest. No distance or displacement is occurring.
   2. Constant speed is when an object is moving at the same rate for the duration of time.

At Rest


Fast


Slow Motion

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Class Notes: Graph Shapes (At rest and Constant Speed)

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Class Notes: Motion Diagrams and Ticker Tape Diagrams

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Class Notes: The Big Five

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Summarize the Reading: 1D Kinematics, Lesson 3 (Method 2a)

Lesson 3

1. What (specifically) did you read that you already understood well from our class discussion? Describe at least 2 items fully.
   1. I understood that a constant slope is a straight line and that a changing slope or acceleration is a curved line. Also, that a positive slope is going from the left bottom and up. A negative slope is going from the left top to the bottom.

1. What (specifically) did you read that you were a little confused/unclear/shaky about from class, but the reading helped to clarify? Describe the misconception you were having as well as your new understanding.
   1. I understood everything in class today.
2. What (specifically) did you read that you still don’t understand? Please word these in the form of a question.
   1. How can you tell the direction of the object by looking at the slope.
3. What (specifically) did you read that was not gone over during class today?
   1. Everything I read was gone over in class today.

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Summarize the Reading: 1D Kinematics, Lesson 4 Notes (Method 2a)

1. What (specifically) did you read that you already understood well from our class discussion? Describe at least 2 items fully.
   1. I understood if the slope is positive then the velocity is positive. Also, I understood the directions of the line in correlation to the velocity, such as constant, rightward velocity and constant, leftward velocity

1. What (specifically) did you read that you were a little confused/unclear/shaky about from class, but the reading helped to clarify? Describe the misconception you were having as well as your new understanding.
   1. I was a little confused on the Area on a v-t graph, but after I read how to do it, I understood it. The area of a velocity vs. Time graph is the displacement.
2. What (specifically) did you read that you still don’t understand? Please word these in the form of a question.
   1. I am a little confused when on reading the graphs when they are accelerating and negative. I just have to practice this. What is a good way to figure out the negative accelerating graphs and which way they are going?
3. What (specifically) did you read that was not gone over during class today?
   1. We did not go over the Area on Velocity vs. time graphs. I learned that all you had to do is take the overall time and overall speed and use the formula for the particular shape.

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Class Activity: Graphing Acceleration

Procedure: We were seeing acceleration patterns by using a ramp, car, and sensor. We put the sensor at the top and at the bottom of the ramp. We let the car just roll down the ramp and push it up the ramp to see what the graphs would look like.

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Class Notes: Increasing and Decreasing Speed Graphs

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Graph Interpretation Worksheet

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Lab: Acceleration on an Incline

Date: 9/16
Lab Partner: Matt Ordover

Objectives:

• What does a position-time graph for increasing speeds look like?
  • It will increase in slope and be steeper.
  • What information can be found from the graph?
    • Position, acceleration, velocity, and how fast the car is going.

Procedure and Materials
Spark tape, spark timer, ramp, dynamics cart, ruler

1. We set up the ramp with one text book, so the whole class would have the same incline
2. we put the spark tape in the spark timer
3. We let the car roll down from the top of the ramp
4. After, we pushed the car up the ramp and let it roll down naturally

Data and Graphs:




Analysis:
a) Interpret the equation of the line (slope, y-intercept) and the R2 value.

1. The linear R^2 value gave me .95 and my polynomial fit gave me .999 which was closer to 1 which shows that the polynomial line is more accurate.

b) Find the instantaneous speed at halfway point and at the end. (You may find this easier to do on a printed copy of the graph. Just remember to take a snapshot of it and upload to wiki when you are done.)
c) Find the average speed for the entire trip.

1. V= d/t
2. The average speed for the entire trip is 35 m/s.

Discussion Questions:

1. What would your graph look like if the incline had been steeper?
   1. The slope of the line would have been steeper for negative and positive acceleration.
   2. What would your graph look like if the cart had been decreasing up the incline?
      1. The line is going away from the axis and as time goes on the slope would decrease.
   3. Compare the instantaneous speed at the halfway point with the average speed of the entire trip
      1. The Instantaneous speed at the half way point of the increasing and decreasing speed is very similar to the speed of the entire trip. The Increasing speed at the halfway point was 33.33 m/s and the Decreasing speed at the halfway point was 35.83 m/s. The average speed for the entire trip was 35 m/s.
         1. Instantaneous Speed:
         2. Increasing: 33.33 m/s
         3. Decreasing: 35.83 m/s
         4. Average Speed:35m/s
            1. 
         5. Explain why the instantaneous speed is the slope of the tangent line. In other words, why does this make sense?
            1. Instantaneous speed is the slope of the tangent line because since that line touches the half way point which is only one point. Since it runs through that specific point the tangent will have the same slope/ speed as the point it runs through.
         6. Draw a v-t graph of the motion of the cart. Be as quantitative as possible.
            1. 

Decreasing



Conclusion:
We found that when the car rolled down the ramp it accelerated and when we pushed the car up the ramp we found that it decelerated when it reached the top. Our hypothesis was correct because an increasing speed position time graph has a steeper slope and its is going away in a positive direction from the origin. The information found from the graph was acceleration, increasing speed and decreasing speed. Sources of error that may have contributed to inaccuracies were when we were measuring we could have used a tape measure. This would have prevented us from having to run out of room on the ruler. Also, we may not have had enough points of decreasing speed on the spark tape because it was hard to get 10. We possibly could have used a bigger ramp to have a larger distance to obtain points.

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Quantitative Graph Interpretation

Question D


Question E

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Lab: Crash Course

9/23/11
Partners: Matt Ordover, Lauren Barinsky, and Garret Almeida.

Purpose: We want to find when a slower constant motion vehicle crashes into a faster constant motion vehicle. Also, we want to find when the faster car would catch up to the slower car. These two cars are placed 1m apart and they are facing the same direction.

Procedure and Materials

Part 2:


Part 1:


Observations






Calculations:
Catch up Test





Crash Test



Discussion Questions

1. Where would the cars meet if their speeds were exactly equal?
   1. For the crash test problem, the cars would meet at 3 meters if their speeds were exactly equal.
   2. For the Catch up problem, the cars would never meet because they would be going the same speed the entire time. They would also keep the same distance between them the entire time.
2. Sketch position-time graphs to represent the catching up and crashing situations. Show the point where they are at the same place at the same time.
   1. 
3. Sketch velocity-time graphs to represent the catching up situation. Is there any way to find the points when they are at the same place at the same time?
   1. Above is the velocity time graph for the catching up situation.

Percent Error


Percent Difference Formula


Percent Difference Chart



Conclusion:
For the Crash Course Lab, my hypothesis was pretty accurate. My calculations were close to the experimental data. This can be shown through finding the percent error was 13.6% for the crash test and for the catching up test it was 3.82%. The information found in this lab was when the Cars would crash which was at about 148 cm and where the faster car would catch up to the slower car. This was at about 147 cm. Some sources of error that may have contributed to inaccuracies are that we had to use a different blue car from the original CMV lab because the original one was not working. Also, The blue car did not move in a straight line, so when we approximated where the cars crashed we were making an imaginary line. The cars did not actually touch each other. For the next lab, we could get cars that moved in straight lines, or we could have put the cars on a track. This would help us get more accurate results because we would be able to see where the cars hit each other.

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Egg Drop Project

Final Device


Description and analysis:
Mass of egg: 60.47g
Mass of Final Device and Egg: 94.77

Delta d= v (initial)t + 1/2at^2
8.5= 0(1.38) + 1/2a(1.38)^2
8.5 = 0+ 1/2(1.90)a
8.5= .952a
a= 8.93 m/s^2

Our final device was made out of straws and hot glue. We made a cube out of straws and on the inside we made a compartment for the egg. On each corner of the device we put 3 short straws to lessen the impact of the eggs fall. We thought this device would work, however, our egg was scrambled. If we had put a parachute on our device it most likely would have been successful. Our devices acceleration was 8.93 m/s^2. The acceleration due to gravity is 9.8 m/s. The acceleration was too high and if we had slowed it down there would be less impact for the egg to take in. If we did this project again, we would put a parachute on our device to slow it down.

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Summarize the Reading: 1D Kinematics, Lesson 5 (Method 1)

Summary 1

Introduction to Free Fall
A free falling object is an object that is falling under the sole influence of gravity. object being acted upon the force of gravity is said to be in a state of free fall. two important motion characteristics:

1. Free-falling objects do not encounter air resistance.
2. All free-falling objects (on Earth) accelerate downwards at a rate of 9.8 m/s/s (often approximated as 10 m/s/s for back-of-the-envelope calculations)

free-falling objects are accelerating downwards at a rate of 9.8 m/s/s, a ticker tape trace or dot diagram of its motion would depict an acceleration. if an object travels downward and speeds up, then its acceleration is downward.
The Acceleration of Gravity
9.8m/s/s is known as the acceleration of gravity is an important quantity that physicists have a special symbol to denote it - the symbol g. slight variations in this numerical value dependent primarily upon on altitude.
g = 9.8 m/s/s, downward
( ~ 10 m/s/s, downward)
If the velocity and time for a free-falling object being dropped from a position of rest were tabulated, then one would note the following pattern.

Time (s)	Velocity (m/s)
0	0
1	- 9.8
2	- 19.6
3	- 29.4
4	- 39.2
5	- 49.0

Representing Free Fall by Graphs

a curved line on a position versus time graph signifies an accelerated motion. A further look at the position-time graph reveals that the object starts with a small velocity (slow) and finishes with a large velocity (fast). Finally, the negative slope of the line indicates a negative (i.e., downward) velocity.
velocity versus time graph for a free-falling object

Observe that the line on the graph is a straight, diagonal line. it would be expected that its velocity-time graph would be diagonal. A further look at the velocity-time graph reveals the object is moving in the negative direction and speeding up. This analysis of the slope on the graph is consistent with the motion of a free-falling object


How Fast? and How Far?

The velocity of a free-falling object that has been dropped from a position of rest is dependent upon the time that it has fallen. The formula for determining the velocity of a falling object after a time of t seconds is
vf = g * t
where g is the acceleration of gravity. The value for g on Earth is 9.8 m/s/s. The above equation can be used to calculate the velocity of the object after any given amount of time when dropped from rest.
The distance that a free-falling object has fallen from a position of rest is also dependent upon the time of fall.

The Big Misconception

"doesn't a more massive object accelerate at a greater rate than a less massive object?" "Wouldn't an elephant free-fall faster than a mouse?".
doesn't a more massive object accelerate at a greater rate than a less massive object? is absolutely not!
the acceleration of an object is directly proportional to force and inversely proportional to mass. Increasing force tends to increase acceleration while increasing mass tends to decrease acceleration. the greater force on more massive objects is offset by the inverse influence of greater mass. all objects free fall at the same rate of acceleration, regardless of their mass.

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Lab:Freely Falling Objects

Purpose/ Objective: What is acceleration due to gravity

Hypothesis: The acceleration due to gravity is -9.8m/s^2. I predict a velocity time graph will look like a diagonal line from the origin and away from the graph. We will find the acceleration from the graph by finding the difference in velocity from one point to another.


Materials: Spark timer, spark tape, a mass, and masking tape


Position and time data from the falling object


Position Time Graph:


Velocity time date for the freely falling object:



Velocity Time Graph:


Class Average: (cm/s^2)


Sample calculation of velocity:


Percent Error


Percent Difference



slope: The slope of the our velocity time graph was 861.69, which was above the class average. This shows that our data was closer to the theoretical value of 9.8m/s^2. this indicates the acceleration.

r^2: Our R^2 value for the position time graph was 1 which shows that our data was basically perfect, but for the velocity time graph the value was .9998. Our data was pretty accurate because this decimal is pretty close to 1. It was 99.9 % accurate.

y-int: You can't set the y intercept to zero because we do not know if the exact initial velocity was zero. The timer could have started a little before or after an initial velocity of zero. We could have started our calculations at not at the first dot on the spark tape because it was in a cluster of dots. Therefore, it was unclear which one was the beginning. If there was friction that is why it would not start at zero. This could have been prevented by using the motion sensor.
Discussion Questions

1. Does the shape of your v-t graph agree with the expected graph? Why or why not?
   1. Yes, my v-t graph agrees with the expected graph. This agrees with the expected graph because a velocity time graph of a steadily freely falling object should be a linear straight line, whether it is increasing or decreasing. My graph was constantly increasing (straight diagonal line).

1. Does the shape of your x-t graph agree with the expected graph? Why or why not?

Yes, the shape of the position time graph does agree with the expected graph because the normal x-t graph of an accelerating object should be curved. This graph was a parabolic curve.

1. How do your results compare to that of the class? (Use Percent difference to discuss quantitatively.)
   1. Our result was 861.69 cm/s^s and the class average was 834.03cm/s^2. Our results were higher than average, which means we were closer to the theoretical yield of 981cm/s^ (which is acceleration due to gravity). Our percent difference was 3.32% which means it was pretty accurate. This is because our acceleration was closer to the theoretical value of 981cm/s^2
2. Did the object accelerate uniformly? How do you know?

Yes because when an object falls its acceleration is the change in velocity and the change in velocity was constant. I can tell by looking out our v-t graph and seeing that the graph is a straight, constant line going away from the origin.

1. What factor(s) would cause acceleration due to gravity to be higher than it should be? Lower than it should be?
   1. Acceleration due to gravity is 9.81cm/s^2. Some factors that would cause acceleration due to gravity to be higher than it should be are if someone was pulling the object down and acting another force upon it. It would be lower if their was something acting on against gravity that would prevent the object from falling freely such as friction.

Conclusion and Analysis:
In conclusion, my hypothesis was correct. In my hypothesis I stated that the acceleration due to gravity is -9.8m/s^2, which is correct. However, our acceleration due to gravity was no -9.98cm/s^2 due to friction. I predicted that the velocity time graph will look like a diagonal line from the origin and away from the graph, which was correct. This was proven correct by looking at the velocity time graph. Our percent error was 1.98% which is pretty accurate. The errors may have occurred if we had a dent or crumple in the spark tape. The spark timer may have missed a dot on the tape because of the imperfections in it. Also, the tape could have gotten stuck in the timer during the experiment. This could be prevented by making sure the tape is laid flat our behind us and it is important to make sure the tape was not turned over at any part of it. We could have measured incorrectly, which some of our results may have been off. This could be prevented by being careful and precise when measuring. Also, we could have started on the wrong dot, which could have messed up our results. This could be prevented by making sure we had plenty of data and making sure we start after the clump of dots from holding the object and starting the timer before we dropped it. The mass that we dropped in this experiment was 100g.

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Free Fall Class Notes